Smoothed Particle Hydrodynamics (SPH) is a fully Lagrangian method, where the ?uid medium is discretized by interaction between particles rather than mesh cells.The basic concept of SPH is that continuous media are represented by discrete particles, whose movement prescribes the ?ow ?eld.The particles have a kernel function to de?ne their range of interaction and the hydrodynamic variable ?elds are approximated by integral interpolations. Meshes are not needed in the simulation, which is a major advantage of SPH over Eulerian methods. The simulations of the incompressible ?ows can beachieved by two methods: (1) approximately simulating incompressible ?ows with a small compressibility called Weakly Compressible SPH; (2) simulating ?ows by enforcing the incompressibility, called Incompressible SPH. In ISPH methods the incompressibility has been generally achieved by the projection method.In the two past decades, WCSPH method has been most widely used in simulations of incompressible ?ows. However, with WCSPH, the pressure ?eld strongly depends on a state equation, generally resulting in large pressure ?uctuations. The accuracy can be improved by remeshing on a uniform grid, which was ?rst introduced by Chaniotis in the context of SPH. But clearly this loses the mesh free characteristic. Moreover, to satisfy the Courant–Friedrichs–Lewy time-step constraint, with a speed of sound in the CFL number expression, the time step is limited to a very small value. In fact, the small density errors in WCSPH method caused non-physical pressure fluctuations which can yield numerical instability. All these considerations led to make a fully incompressible algorithm in SPH.In this thesis, a new Incompressible Smoothed Particle Hydrodynamics (ISPH) algorithm based on projection method is introduced. This algorithm has two steps. In the first step, the incompressibility of fluid is maintained in regard to the changes of intermediate and initial particles densities at the first half-time step (stability step). In the second step, by computing the divergence of the intermediate secondary velocity at the second half-time step (accuracy step), the incompressibility is satisfied completely.This algorithm is compered with WCSPH , Incompressible SPH based on keeping divergence free velocity (ISPH_DF) and Incompressible SPH based on keeping density invariance (ISPH_DI) by simulating lid-driven cavity flow. The results are shown that this new algorithm is more accurate and more atable in comparison with WCSPH, ISPH_DF and ISPH_DI. Also, it can simulate Incompressible flow with the larger than time step. To investigate the performance of code based on new algorithm two problems such as 2-D dam beak flow and moving a square in a rectangular fluid domain are simulated. Keywords: SPH, Incompressible flow, Projection method, lid-driven cavity flow